Modeling of a Fluid with Pressure-Dependent Viscosity in Hele-Shaw Flow

We investigate the Hele-Shaw flow of fluids whose viscosity depends on pressure, i.e., piezo-viscous fluids, near the tip of a sharp edge. In particular, we consider both cases of two-dimensional symmetric and antisymmetric flows. To obtain the pressure field, we provide a procedure that is based on...

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Main Authors: Benedetta Calusi, Liviu Iulian Palade
Format: Article
Language:English
Published: MDPI AG 2024-10-01
Series:Modelling
Subjects:
Online Access:https://www.mdpi.com/2673-3951/5/4/77
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author Benedetta Calusi
Liviu Iulian Palade
author_facet Benedetta Calusi
Liviu Iulian Palade
author_sort Benedetta Calusi
collection DOAJ
description We investigate the Hele-Shaw flow of fluids whose viscosity depends on pressure, i.e., piezo-viscous fluids, near the tip of a sharp edge. In particular, we consider both cases of two-dimensional symmetric and antisymmetric flows. To obtain the pressure field, we provide a procedure that is based on the method of separation of variables and does not depend on a specific choice of the expression for the pressure-dependent viscosity. Therefore, we show the existence of a general procedure to investigate the behavior of piezo-viscous fluids in Hele-Shaw flow and its solution near a sharp corner. The results are applied to the case of an exponential dependence of viscosity on pressure as an example of exact solutions for the pressure field.
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spelling doaj-art-a568065eaed24cb7b4e2ba121f5f69392025-08-20T02:01:10ZengMDPI AGModelling2673-39512024-10-01541490150410.3390/modelling5040077Modeling of a Fluid with Pressure-Dependent Viscosity in Hele-Shaw FlowBenedetta Calusi0Liviu Iulian Palade1Dipartimento di Matematica e Informatica “Ulisse Dini”, Università degli Studi di Firenze, Viale Morgagni 67/a, 50134 Firenze, ItalyInstitut Camille Jordan CNRS UMR 5208, INSA-Lyon & Pôle de Mathématiques, Université de Lyon, 21 Avenue Jean Capelle, 69621 Villeurbanne Cedex, FranceWe investigate the Hele-Shaw flow of fluids whose viscosity depends on pressure, i.e., piezo-viscous fluids, near the tip of a sharp edge. In particular, we consider both cases of two-dimensional symmetric and antisymmetric flows. To obtain the pressure field, we provide a procedure that is based on the method of separation of variables and does not depend on a specific choice of the expression for the pressure-dependent viscosity. Therefore, we show the existence of a general procedure to investigate the behavior of piezo-viscous fluids in Hele-Shaw flow and its solution near a sharp corner. The results are applied to the case of an exponential dependence of viscosity on pressure as an example of exact solutions for the pressure field.https://www.mdpi.com/2673-3951/5/4/77Hele-Shaw flowsymmetrical and antisymmetrical flowslubrication approximationpressure-dependent viscositypiezo-viscous fluids
spellingShingle Benedetta Calusi
Liviu Iulian Palade
Modeling of a Fluid with Pressure-Dependent Viscosity in Hele-Shaw Flow
Modelling
Hele-Shaw flow
symmetrical and antisymmetrical flows
lubrication approximation
pressure-dependent viscosity
piezo-viscous fluids
title Modeling of a Fluid with Pressure-Dependent Viscosity in Hele-Shaw Flow
title_full Modeling of a Fluid with Pressure-Dependent Viscosity in Hele-Shaw Flow
title_fullStr Modeling of a Fluid with Pressure-Dependent Viscosity in Hele-Shaw Flow
title_full_unstemmed Modeling of a Fluid with Pressure-Dependent Viscosity in Hele-Shaw Flow
title_short Modeling of a Fluid with Pressure-Dependent Viscosity in Hele-Shaw Flow
title_sort modeling of a fluid with pressure dependent viscosity in hele shaw flow
topic Hele-Shaw flow
symmetrical and antisymmetrical flows
lubrication approximation
pressure-dependent viscosity
piezo-viscous fluids
url https://www.mdpi.com/2673-3951/5/4/77
work_keys_str_mv AT benedettacalusi modelingofafluidwithpressuredependentviscosityinheleshawflow
AT liviuiulianpalade modelingofafluidwithpressuredependentviscosityinheleshawflow